Langfeldt, FelixFelixLangfeldtGleine, WolfgangWolfgangGleineEstorff, Otto vonOtto vonEstorff2020-11-132020-11-132015-04-11Journal of Sound and Vibration (349): 315-329 (2015)http://hdl.handle.net/11420/7833An analytical model for the transmission loss calculation of thin rectangular and circular membranes loaded with rigid masses of arbitrary shape, the so-called membrane-type acoustic metamaterials, is presented. The coupling between the membrane and the added masses is introduced by approximating the continuous interaction force with a set of discrete point forces. This results in a generalized linear eigenvalue problem that is solved for the eigenfrequencies and eigenvectors of the coupled system. The concept of the effective surface mass density is employed to calculate the low-frequency transmission loss using the obtained eigenpairs. The proposed model is verified using numerical data from a finite element model and the convergence behavior of the point matching approach is investigated using Richardson extrapolation. Finally, a method based upon the grid convergence index for estimating the error that is introduced due to the point matching approach is presented.en0022-460X2015315329Academic PressTechnikJournal Article10.1016/j.jsv.2015.03.037Journal Article